Dual neighborhood systems and polars in locally convex cones

Abstract

In this paper, we define dual (abstract) neighborhood systems for locally convex cones. Also we consider three types of different polars and study some relations of them with bounded sets in locally convex cones.

Keywords

• locally convex cones,polar,duality

References

1. D. Ayaseh and A. Ranjbari, Bornological locally convex cones, Matematiche (Catania) 69 (2), 267-284, 2014.
2. D. Ayaseh and A. Ranjbari, Locally convex quotient lattice cones, Math. Nachr. 287 (10), 1083-1092, 2014.
3. D. Ayaseh and A. Ranjbari, Bornological Convergence in Locally Convex Cones, Mediterr. J. Math. 13 (4), 1921-1931, 2016.
4. K. Keimel and W. Roth, Ordered cones and approximation, Lecture Notes in Math- ematics 1517, Springer-Verlag, Berlin, 1992.
5. G.D. Plotkin, A Domain-Theoretic Banach-Alaoglu Theorem, Math. Struct. Com- pute. Sci. 16 (2), 299-313, 2006.
6. A. Ranjbari, Strict inductive limits in locally convex cones, Positivity 15 (3), 465-471, 2011.
7. A. Ranjbari and H. Saiflu, Projective and inductive limits in locally convex cones, J. Math. Anal. Appl. 332 (2), 1097–1108, 2007.
8. W. Roth, Hahn-Banach type theorems for locally convex cones, J. Austral. Math. Soc. Ser. A 68 (1), 104-125, 2000.

9. W. Roth, Operator-valued measures and integrals for cone-valued functions, Lecture Notes in Mathematics 1964, Springer-Verlag, Berlin, 2009.
10. W. Roth, Locally convex quotient cones, J. Convex Anal. 18 (4), 903-913, 2011.